We present spectral and timing analyses of Nuclear Spectroscopic Telescope Array (NuSTAR) observations of the accreting X-ray pulsar 2RXP J130159.6-635806. The source was serendipitously observed during a campaign focused on the gamma-ray binary PSR B1259-63 and was later targeted for a dedicated observation. The spectrum has a typical shape for accreting X-ray pulsars, consisting of a simple power law with an exponential cutoff starting at ∼7 keV with a folding energy of keV. There is also an indication of the presence of a 6.4 keV iron line in the spectrum at the significance level. NuSTAR measurements of the pulsation period reveal that the pulsar has undergone a strong and steady spin-up for the last 20 years. The pulsed fraction is estimated to be , and is constant with energy up to 40 keV. The power density spectrum shows a break toward higher frequencies relative to the current spin period. This, together with steady persistent luminosity, points to a long-term mass accretion rate high enough to bring the pulsar out of spin equilibrium.